I am listening to the audiobook The Horse, the Wheel, and Language: How Bronze Age Riders from the European Steppes Shaped the Modern World by David W. Anthony. I have read a few similar books describing how linguists have partially reconstructed the Proto-Indo-European language.
Looking through our library at home, I found a copy of In Search of the Indo-Europeans: Language, Archaeology, and Myth by J. P. Mallory (1989, Thames and Hudson), which I should read again.
But what if I wanted more than introduction to this subject? It seems that I would need to read technical books on linguistics and philology. Linguistics is a very broad field. Where to start? For my future reference, I have listed results from an internet search.
Open Textbook Library offers Essentials of Linguists, 2nd Edition by Catherine Anderson, Bronwyn Bjorkman, and Derek Denis.
Cambridge Textbooks in Linguistics comprises 77 books. Language Change by Joan Bybee and Evolutionary Linguistics by April McMahon and Robert McMahon might be two good books to start with.
This book might be too introductory: The First Word: The Search for the Origins of Language by Christine Kenneally (published in 2008).
The Handbook of Linguistics, edited by Mark Aronoff and Janie Rees-Miller looks like a useful collection of chapters on various topics in linguistics including linguistic anthropology and ethnolinguistics. I might start with this book for a more detailed introduction to the various subfields of linguistics.
The Handbook of English Linguistics, edited by Bas Aarts, April McMahon, and Lars Hinrichs, appears to contain technical introductions to various aspects of the English language.
An Introduction to Language and Linguistics by Ralph W. Fasold and Jeff Connor-Linton has a chapter on computational linguistics.